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Inference on Common Trends in Functional Time Series
Inference on Common Trends in Functional Time Series
Morten Ørregaard Nielsen, Aarhus University
Abstract
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series of interest takes values in a subspace of possibly unknown dimension. This has wide applicability in practice; for example, to the case of cointegrated vector time series that are either high-dimensional or of finite dimension, to high-dimensional factor model that includes a finite number of nonstationary factors, to cointegrated curve-valued (or function-valued) time series, and to nonstationary dynamic functional factor models. We include two empirical illustrations to the term structure of interest rates and labor market indices, respectively.
Understanding Regressions with Observations Collected at High Frequency over Long Span
Understanding Regressions with Observations Collected at High Frequency over Long Span
Ye Lu, University of Sydney
Abstract
In this paper, we analyze regressions with observations collected at small time intervals over a long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast relative to T → ∞. Such a phenomenon is indeed what is frequently observed in practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robust version of the Wald test with an appropriate long-run variance estimate. This is supported, strongly and unambiguously, by our empirical illustration using the regression of long-term on short-term interest rates.
Convergence in distribution of quantile, Lorenz and P-P processes via the delta method
Convergence in distribution of quantile, Lorenz and P-P processes via the delta method
Brendan K. Beare, University of Sydney
Abstract
We establish a necessary and sufficient condition for the quantile process based on iid sampling to converge in distribution in the space $L^1(0,1)$. The condition is that the quantile function is locally absolutely continuous on the open unit interval and satisfies a slight strengthening of square integrability. For a nonzero population mean, convergence in distribution of the quantile process in $L^1(0,1)$ is shown to be sufficient, but not necessary, for convergence in distribution of the associated Lorenz process in $C[0,1]$. We further establish a necessary and sufficient condition for the P-P process based on iid sampling from two populations to converge in distribution in $L^1(0,1)$. The condition is that the P-P curve is locally absolutely continuous on the open unit interval. All demonstrations of convergence in distribution are achieved using the delta method, and therefore validate a bootstrap approximation to the relevant process as a byproduct.
Increased persistence of warm and wet winter weather in north-western Europe due to trends towards strongly positive NAO
Increased persistence of warm and wet winter weather in north-western Europe due to trends towards strongly positive NAO
Julia Schaumburg, Vrije Universiteit Amsterdam
Abstract
The winter North Atlantic Oscillation (NAO) has seen a long-term trend towards strongly positive values over the last decades. Although this shift aligns with climate model projections under scenarios of strong greenhouse gas forcing, the observed changes exceed the range predicted by these models. While the relationship between the NAO and temperature or precipitation patterns is well-established, the shift’s impact on weather persistence remains unclear and may influence different parts of the temperature distribution and the probability of precipitation in distinct ways. We introduce statistical models to capture this distributional heterogeneity. When comparing 1950–1980 with 1990–2020, we find that both warm temperature and precipitation persistence have increased significantly in north-western Europe in winter. For precipitation, this implies that when the NAO index is strongly positive, the likelihood of over two weeks of precipitation within three weeks has roughly tripled over north-western Europe, strongly amplifying flood risk.
Cross-Temporal Forecast Reconciliation at Digital Platforms with Machine Learning
Cross-Temporal Forecast Reconciliation at Digital Platforms with Machine Learning
Ines Wilms, Maastricht University
Abstract
Platform businesses operate on a digital core and their decision making requires high-dimensional accurate forecast streams at different levels of cross-sectional (e.g., geographical regions) and temporal aggregation (e.g., minutes to days). It also necessitates coherent forecasts across all levels of the hierarchy to ensure aligned decision making across different planning units such as pricing, product, controlling and strategy. Given that platform data streams feature complex characteristics and interdependencies, we introduce a non-linear hierarchical forecast reconciliation method that produces cross-temporal reconciled forecasts in a direct and automated way through the use of popular machine learning methods. The method is sufficiently fast to allow forecast-based high-frequency decision making that platforms require. We empirically test our framework on a unique, large-scale streaming dataset from a leading on-demand delivery platform in Europe.
Nearest neighbor matching
Nearest neighbor matching
Fang Han, University of Washington
Abstract
In two landmark Econometrica papers, Abadie and Imbens proved that the nearest neighbor (NN) matching estimator of the average treatment effect, when using a fixed number of neighbors, is asymptotically normal but semiparametrically inefficient and bootstrap inconsistent. In this talk, I will show that the same NN matching estimator becomes asymptotically normal, doubly robust, semiparametrically efficient, and bootstrap consistent as long as we force the number of NNs to diverge with the sample size.Page updated
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